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Overconfident : Confident opponents gain Armor. Aghast : Terrified opponents gain Armor. Lament : Saddened opponents gain Speech Defense. Nodes circles indicate the geographic locations visited by the individual, and each link denotes a travel observed between two locations. When the total r g is small, the two most important locations red and blue are close to each other for both two-explorers and two-returners. As the total radius increases the behaviour of two-returners and two-explorers starts to differ; for two-returners, the two most important locations move away from each other; for two-explorers, they stay close and other clusters of locations emerge far from the centre of mass the grey cross.
We compare our findings with the results produced by the exploration and preferential return EPR individual mobility model 4 , a state-of-the-art model that accurately captures the visitation frequency of locations, the distribution of the radius of gyration across the population and its growth with time ultraslow diffusion.
The model incorporates two competing mechanisms, the exploration of new locations and the return to previously visited locations. We use the EPR model to simulate the mobility of 67, synthetic individuals see Box 1 , and Supplementary Notes 11 and 12 and computed for each synthetic individual the total r g and. As shown in Fig. The difference between the empirical and synthetic data is especially clear when we explore P s k Fig.
Thus, the EPR model overestimates by more than an order of magnitude the number of locations needed to accurately estimate the total radius of gyration. Contrarily to the empirical results, in the EPR model there is no significant correlation between total r g and the sum of the distances of the k- th most visited locations Pearson correlation coefficient is close to zero , neither for k -returners nor for k -explorers see Supplementary Fig.
The insets in a,d magnify the plot at smaller values of the radii of gyration. Plots c , f show how the number of k -returners and k -explorers changes with k for EPR model and d -EPR model, respectively. The observed discrepancies between the empirical data and the EPR model could arise from the fact that in the model individuals can travel arbitrarily large distances, increasing their total r g with each jump.
To correct for this limitation, we propose the d -EPR model, in which an individual selects a new location to visit depending on both its distance from the current position, as well as its relevance measured as the overall number of calls placed by all individuals from that location. This modification is justified by the accuracy of the gravity model to estimate origin-destination matrices at the country level 34 , 35 , 36 , Consequently, the correlation plot of versus total r g displays the empirically observed split into returners and explorers Fig.
Hence, the d -EPR model of human mobility reproduces the key features of the aggregated mobility patterns in a confined geographical space, accounting for the two classes of individuals, returners and explorers. The mechanism underlying the model can be easily understood: when a traveller returns, she is attracted to previously visited places with a force that depends on the relevance of such places at an individual level. In contrast when a traveller explores, she is attracted to new places with a force that depends on the relevance of such places at a collective level.
Our findings are particularly relevant in two contexts: the geographical spreading of epidemics and social interactions. Obviously, the wider the range of mobility, the faster will the virus diffuse over the population. The question is, how does the presence of the two mobility profiles uncovered above affect the spreading pattern? We observe that the trajectory of explorers is distributed over a larger territory, as they visit more locations, cover a larger geographic area and have a higher r g t with respect to returners. We also assess the different role the returners and explorers play in diffusion and spreading processes by considering the global mobility networks generated by individual mobility.
The global mobility network is a graph whose nodes are locations and edges indicate the existence of at least one trip between two locations. To be specific, we focus on Tuscany, estimating the mobility of each individual through the GPS data and the number of residents in the locations through the official census cells provided by the ISTAT.
We compute each of the 10 networks 1, times, randomly choosing 10, individuals with different proportion of two-returners and two-explorers, and obtaining 1, values for the invasion threshold for each network Supplementary Note 16 , Supplementary Fig. We observe that the mean diffusion invasion threshold increases with the fraction of explorers in the random population. Here we bring a further contribution by showing that individuals of the two profiles, returners and explorers, tend to engage in social interactions preferably with individuals of the same profile.
In other words, individuals who communicate with each other are more likely to belong to the same mobility group than by chance. As we consider the n -th most called contact and compare the fraction of individuals with the n -th best friend in the same mobility group, we find that the observed fractions are significantly higher than those obtained by chance for all n up to 15, as shown in Fig.
Our findings reveal the existence of a strong correlation between the mobility behaviour of individuals and their social relationships, although further experiments are needed to understand whether this can be interpreted as a homophily or influence effect. The dashed line indicates the real fraction of two-returners two-explorers whose best friend is a two-returner two-explorer. We observe that individuals that communicate with each other are more likely to belong to the same mobility group than by chance.
We observe that the observed the fractions are significantly higher RR and EE or significantly lower ER and RE than those obtained by chance for all n up to Here we report the existence of two distinct profiles characterizing human mobility: returners and explorers. Returners limit much of their mobility to a few locations, hence their recurrent and overall mobility are comparable.
In contrast, the mobility of explorers cannot be reduced to few locations. These patterns cannot be explained by the EPR model of human mobility, unable to distinguish returners from explorers. We show that by incorporating a gravity model into the EPR mechanism, we can recover the two classes, the obtained extended model coming closer to the empirical observations characterizing the two profiles.click
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We show that explorers and returners play different roles in the disease spreading and that they tend to engage in social interactions with individuals with similar mobility profiles. The emerging profiles of returners and explorers offer another step towards deriving accurate models of human mobility, capable of generating realistic simulations, predictions and what-if reasoning in context such as energy consumption, gas emission and urban planning How to cite this article: Pappalardo, L.
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